The gradient method for unconstrained optimization problems requires the tuning of more parameters than the gradient method for quadratic functions. We maintain the choices made in [1]} and set \(\beta _{\min } = 10^{-30}\) , \(\beta _{\max } = 10^{30}\) , \(c_{\rm {ls}} = 10^{-4}\) , \(\sigma _{\rm {ls}} = \frac{1}{2}\) , \(M = 10\)  and \(\beta _{0}^{\rm {}} = 1\) . One may argue that the bounds on the stepsize are extremely large: the aim of this choice is to accept the BB stepsize as frequently as possible. Again the algorithm stops when \(\Vert \mathbf {g}_k\Vert  \le {\sf tol}\,\Vert \mathbf {g}_0\Vert \) , with \({\sf tol} = 10^{-8}\) , or when \(5\cdot 10^4\)  iterations are reached. All different steps in Table REF  are tested.
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